The following chart plots the average performance of the FTSE 100 Index during January since 1984.

As can be seen, historically the market tends to rise for the first two or three days in January and then sells off quite strongly over the following two weeks. The second week of January is the weakest week for the market in the whole year. Then, around the middle of the third week, the market has tended to rebound sharply.

After market close on 30 November 2016 FTSE Russell confirmed the following changes to the FTSE 100 and FTSE 250 indices. The changes will be implemented at the close Friday, 16 December 2016 and take effect from the start of trading on Monday, 19 December 2016.

1946-2016

The chart below plots the FTSE All Share Index from 1946 to the present day.

The Y-scale is logarithmic, which presents percentage (rather than absolute) changes better over long periods, and so is more suitable for long-term charts.

The straight line is a line of best fit calculated by regression analysis.

Observations-

The R2 for the line of best fit is 0.96, which is impressively high for such a simple model (i.e. the line of best fit fairly accurately approximates the real data points).

The FTSE All Share Index fluctuated closely around the trend line (line of best fit) from 1946 to 1973; it then traded consistently below the trend line until 1983, when it crossed over to trade above the trend line until 2001. From 2001 the Index was close to the trend, but then in 2008 fell significantly below it and has yet to revert to the long-term trend line.

Forecasts

The equation of the line of best fit in the chart above (with a little more precision) is-

y = 0. 846531e0.000207x

This equation allows us to make forecasts for the FTSE All Share Index. It is, in effect, the Holy Grail, the key to the stock market – as simple as that!

For example, at the time of writing the FTSE All Share Index is 3664 while the above equation forecasts a value today (according to the long-term trend line) of 5878. This suggests the index is currently under-priced relative to the long-term trend line. But as can be seen in the above chart the index can spend long periods trading above or below the long-term trend line.

Now, if we think that the trend of the market in the last 70 years will broadly continue, then we can use the equation to forecast the level of the FTSE All Share Index in the future. And this is what has been done in the following table. Equivalent forecasts for the FTSE 100 Index have also been given.

Date

FTAS Forecast

FTSE 100 Forecast

Chng(%)

Dec 2017

6,403

11,762

75

Dec 2020

8,036

14,761

119

Dec 2030

17,128

31,460

367

Dec 2040

36,513

67,068

897

The equation says that the trend line value for FTSE 100 at the end 2017 will be 11,762 (75% above its level in November 2016,).

By end 2020 the forecast is for a FTSE 100 level of 14,761 (+119%), and by end 2040 the equation forecasts a FTSE 100 trend value of 67,068 (+897%).

So, that’s easy.

Well, except this…

1920-2016

We will now look at a trend line calculated from data 1920 to 2016.

First, here is the chart from 1920 with its trend line.

In this case, the R2 is 0.69, quite a bit lower than than the data from 1946 (i.e. the calculated trend line is not such such a good fit for the actual data).

Again we can use the equation of the trend line to forecast trend values for future dates.

Date

FTAS Forecast

FTSE 100 Forecast

Chng(%)

Dec 2017

4,116

7,652

14

Dec 2020

5,006

9,195

37

Dec 2030

9,230

16,953

152

Dec 2040

17,020

31,263

365

Whereas for the data from 1946 forecast a FTSE 100 level of 11,762 at end of 2017, the 1920 data forecasts a level of 7,652 (14% above the current level).

As can be seen above, the trend-line equation is very sensitive to the sample data (i.e. in this case, the choice of start date).

So, which trend do you prefer, that from 1920 or from 1946?

The above is partly an extract from the new 2017 edition of The Harriman Stock Market Almanac.

We first looked at this in 2013 (in this article), so time to see if anything has changed.

First, the following updates the chart to 2016 plotting Tuesday returns for the FTSE 100 Index split by whether the previous day’s returns were positive or negative. Two time periods are considered: 1984-2016 and 2000-2016.

For example, for the longer period, the average return on Tuesday when Monday was up is 0.02%, while the average Tuesday return when Monday was down is 0.09%.

While the figures have marginally changed from the previous study in 2013, the overall finding is the same: namely that the theory that Tuesday reverses Monday does not seem to hold. Since 1984 it has done so when Monday returns have been negative, but not when they have been positive.

As in the 2013 study, the theory has been valid for the market since 2000.

The previous study suggested that further analysis might include a filter on the size of the Monday returns. This is done in the following chart, where Tuesday returns are only considered if Monday’s returns were beyond a certain threshold (i.e. of a certain size). The (arbitrary) threshold chosen was 1 standard deviation for Monday’s returns.

It can be seen that limiting the analysis of Tuesday returns to just large movements on Monday (i.e. beyond 1 standard deviation) does help the reversal theory. In this case, if the market rises on Monday, then on average it falls the following day (albeit a pretty small average fall), and if the market falls on Monday, the market rises (fairly strongly) on the Tuesday.

Let’s now look at how the theory has been holding up in recent years.

Recent years

The following chart is similar in design to the previous charts, but this time it plots the reversal results for the discrete years 2013 – 2016.

First, when the market is up on Monday, all four of the past four years has failed to support the reversal theory as Tuesday has followed with positive returns as well. When Mondays are down, in three of the past four years Tuesdays have seen positive average returns (the exception being 2015).

Exploiting the reversal effect

OK, so how to exploit this?

The following chart plots the cumulative value of a portfolio that invests in the FTSE 100 just on Tuesdays when the previous day saw negative returns. For the rest of the time it is in cash.

In the 2013 study a variant portfolio was also considered, that as well as going long Tuesdays following negative Mondays also went short Tuesdays following positive return Mondays. There’s currently not much point in considering this as the reversal effect is not working for positive Mondays.

So, instead the variant second strategy studied here is as above (i.e. long Tuesday following a negative Monday) but with a 1 standard deviation filter applied to the Monday return (i.e. the strategy only goes long on Tuesday if the Monday negative return is a greater than 1 standard deviation return).

Since 2000 it can be seen that the simple long Tuesday strategy out-performs the benchmark buy-and-hold FTSE 100 portfolio. The variant 1SD strategy only marginally out-performs the simple long Tuesday strategy, but does so with with a greatly reduced volatility.

We have previously looked at data to see if there are any discernible patterns in market returns by day of the week. The following table presents another way of studying this.

The table shows the daily returns of the FTSE 100 Index for every day so far in 2016 (up to last Friday, 28 Oct). Positive returns are highlighted in green, negative returns in red. (White cells indicate a market holiday.)

Observations:

So far in 2016 the longest run of positive (or negative) returns for a day started in the 10th week of the year when day returns for eight consecutive Wednesdays were positive.

For 11 weeks, the day returns on Fridays were the opposite sign to that on the previous day (Thursday). This run ended last Friday (when both Thursday and Friday saw positive returns).

Historically, the last trading day of October has been the strongest LTD of any month in the year. Since 1984 the market has on average risen 0.46% on the LTD of October, with positive returns in 69% of all years.

The following chart shows the FTSE 100 Index returns for every October LTD since 1984.

As can be seen on the chart the market only fell twice on the October LTD in the 19 years from 1984 to 2002. One possible reason for this may have been that November is the start of the strong six month period of the year (this is part of the Sell in May effect), and investors could have been buying equities at this time in anticipation of that.

However, in recent years this pattern of behaviour has changed. Quite dramatically so – in the last seven years the market has only risen once on the October LTD. Last year (2015) the FTSE 100 Index was down 0.5% on the last trading day of October.

Analysis of the daily close of the FTSE 100 Index and the day’s high and low.

The following table shows the frequency with which the FTSE 100 closes within a certain percentage of the high (or low) of the day. For example, since 1985 the FTSE 100 Index has closed within 10% of its daily high 20.8% of all days, and it has closed within 1% of its low 5.6% of all days.

10%

5%

1%

Top (%)

20.8

15.1

9.8

Bottom (%)

14.5

9.6

5.6

It’s interesting to note that for one in 10 days the index closes within 1% of its high for the day.

The following day

Continuing this analysis of where the index closes relative to the Hi-Lo range of the day, the following table shows the performance of the FTSE 100 Index on the following day.

For example, on the days when the index closes within 10% of its low for the day on average the index return is -0.005% the following day; and when the index closes within 1% of its high for the day on average the index return is 0.167% the following day.

The following chart shows the ratio of the FTSE 250 Index divided by the FTSE 100 Index since 1985. For example, yesterday’s close for the FTSE 250 Index was 18,342.1 and for the FTSE 100 Index it was 7074.3; dividing the former by the latter gives a ratio value of 2.59 (the last value plotted on the chart).

As can be seen, the ratio fluctuated in a sideways range from 1985 to 1999. And then the great out-performance of the FTSE 250 over the FTSE 100 began (on 18 Jan 1999 to be precise).

Over the following 16 years to today, while the FTSE 100 Index increased 16%, the FTSE 250 gained 274%.

The following chart zooms in to show the FTSE 250/100 ratio for the more recent period since 21012-2016.